Now I shall try to give you an idea of the way in which physicists at present endeavour to overcome this failure. One might term it an ‘emergency exit’, though it was not intended as such, but as a new theory. I mean, of course, wave mechanics. (Eddington called it ‘not a physical theory but a dodge—and a very good dodge too’.) The situation is about as follows. The observed facts (about particles and light and all sorts of radiation and their mutual interaction) appear to be repugnant to the classical ideal of a continuous description in space and time. (Let me explain myself to the physicist by hinting at one example: Bohr's famous theory of spectral lines in 1913 had to assume that the atom makes a sudden transition from one state into another state, and that in doing so it emits a train of light waves several feet long, containing hundreds of thousands of waves and requiring for its formation a considerable time. No information about the atom during this transition can be offered.) So the facts of observation are irreconcilable with a continuous description in space and time 5 it just seems impossible, at least in many cases.
Now I shall try to give you an idea of the way in which physicists at present endeavour to overcome this failure. One might term it an ‘emergency exit’, though it was not intended as such, but as a new theory. I mean, of course, wave mechanics. (Eddington called it ‘not a physical theory but a dodge—and a very good dodge too’.) The situation is about as follows. The observed facts (about particles and light and all sorts of radiation and their mutual interaction) appear to be repugnant to the classical ideal of a continuous description in space and time. (Let me explain myself to the physicist by hinting at one example: Bohr's famous theory of spectral lines in 1913 had to assume that the atom makes a sudden transition from one state into another state, and that in doing so it emits a train of light waves several feet long, containing hundreds of thousands of waves and requiring for its formation a considerable time. No information about the atom during this transition can be offered.) So the facts of observation are irreconcilable with a continuous description in space and time 5 it just seems impossible, at least in many cases.
Now I shall try to give you an idea of the way in which physicists at present endeavour to overcome this failure. One might term it an ‘emergency exit’, though it was not intended as such, but as a new theory. I mean, of course, wave mechanics. (Edding-ton called it ‘not a physical theory but a dodge— and a very good dodge too’.) The situation is about as follows. The observed facts (about particles and light and all sorts of radiation and their mutual interaction) appear to be repugnant to the classical ideal of a continuous description in space and time. (Let me explain myself to the physicist by hinting at one example: Bohr's famous theory of spectral lines in 1913 had to assume that the atom makes a sudden transition from one state into another state, and that in doing so it emits a train of light waves several feet long, containing hundreds of thousands of waves and requiring for its formation a considerable time. No information about the atom during this transition can be offered.) So the facts of observation are irreconcilable with a continuous description in space and time; it just seems impossible, at least in many cases. On the other hand, from an incomplete description—from a picture with gaps in space and time—one cannot draw clear and unambiguous conclusions; it leads to hazy, arbitrary, unclear thinking—and that is the thing we must avoid at all costs! What is to be done?
Introduction When I was a student I had much difficulty with quantum mechanics. It was comforting to find that even Einstein had had such difficulties for a long time. Indeed they had led him to the heretical conclusion that something was missing in the theory: ‘I am, in fact, rather firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this (theory) operates with an incomplete description of physical systems.’ More explicitly, in ‘a complete physical description, the statistical quantum theory would … take an approximately analogous position to the statistical mechanics within the framework of classical mechanics …’. Einstein did not seem to know that this possibility, of peaceful coexistence between quantum statistical predictions and a more complete theoretical description, had been disposed of with great rigour by J. von Neumann. I myself did not know von Neumann's demonstration at first hand, for at that time it was available only in German, which I could not read. However I knew of it from the beautiful book by Born, Natural Philosophy of Cause and Chance , which was in fact one of the highlights of my physics education. Discussing how physics might develop Born wrote: ‘I expect … that we shall have to sacrifice some current ideas and to use still more abstract methods. However these are only opinions.
Abstract With the failure of classical physics to explain the experimentally observed black body radiation spectrum, the photoelectric effect and the existence of narrow spectral lines in the light emitted by excited atoms, physicists were forced to reach out for new ideas. Following Planck’s initial “drastic hypothesis” of light “quanta”, Einstein led the way in exploring some of the myriad implications of this idea. In particular, the study of fluctuations led to a new understanding of the interaction of electromagnetic radiation with atoms. Einstein invented the photon by showing, through fluctuation studies, that light emitted by atoms must be in the form of plane waves. These ideas led to the first notions regarding the quantization of matter and its dynamics.
The new physics just described was still based largely on Newtonian ideas. Indeed, in its theoretical aspects, it might not unfairly be described as a final attempt to explain the world in materialistic terms—as particles being pushed and pulled about in space and time. Nevertheless, the new physics had found it necessary to abolish most of the forces of pushing and pulling, replacing the gradual changes of motion of the particles under these forces by sudden and unpredictable jumps. These appeared to involve violations of the law of causality, both in the disintegration of radioactive atoms and also in the internal changes of ordinary atoms. We seemed to see Fate defying this law as she picked out certain atoms for disintegration or collapse and, by her apparently capricious acts, sent the universe along one path or another according to her whim. On such lines the new physics had explained many phenomena which had hitherto seemed inexplicable, but it had by no means met with complete success. For instance, while it gave a perfect interpretation of the simplest spectrum of all, namely that of the hydrogen atom, it failed with more complex spectra. This was not necessarily a fatal objection; a few emendations and possibly a few new ad hoc assumptions might have effected a complete reconciliation, although this seems improbable.
In a period when a limited domain of physical phenomena is exciting wide fervent interest and commanding intensive study, and continues for years to monopolize the attention of many brilliant theorists, sometimes it is the fortune of an ingenious mind to express or interpret or picture the already-discovered laws in a new way which makes so greatly favourable an impression, that in a moment it sweeps its rivals from the field. The new theory may not lead to more or better agreements with experience than did its predecessors; it need not make predictions which they were incapable of making; its mathematical processes may be identical with theirs, the old symbols reappearing with new names in the old equations. Contrariwise it may be born well endowed with these advantages which normally decide the contest between old theories and new, yet owe its victory not to them at all. It triumphs because it seems natural or sensible or reasonable or elegant or beautiful-words said of a theory which fulfils some deep-seated demand or evades some deep-rooted prejudice in the minds of its judges. Later its vogue may pass, not through the disclosure of any intrinsic defect, but because the physicists of the rising generation do not share the prejudices and the predilections of those who first applauded it. The kinetic theory of gases was welcomed by a generation which wished to believe in atoms; the electromagnetic theory by people prejudiced against the notion of action at a distance; the quantum-theory has always had to do battle against those who yearn for continuity in their images of Nature, and the theory to which these pages are devoted has captivated the world of physics in a few brief months because it seems to promise a fulfilment of that long-baffled and insuppressible desire.
Abstract In the present work the wave mechanics are applied to the discussion of a collision problem of a more complicated type than has, I think, hitherto been done. Though there is nothing very new in the process it is rather interesting to see how a wave function behaves which involves two bodies, and is therefore outside our ordinary space intuitions. But the work had a much more general aim, as an attempt to see whether a sharper line of demarcation could be drawn between the particle-like and the wave-like properties of matter. Put briefly, I take a problem which would be regarded at first sight as irreconcilable with a pure wave theory, but thoroughly typical of the behaviour of particles, and show how in fact the correct result arises naturally from the consideration of wave alone. I have been led in this way to certain not very original speculation on the basis of the quantum theory and these are given at the end of the paper. These are not in the least intended to be a general formulation of the theory, but rather as an examination of a particular type of attempted formulation. I fear that the views expressed will be found partly obvious and perhaps partly inconsistent or even erroneous. My excuse for giving them is that the quantum theory seem already sufficiently developed for us to attempt something more than a mathematical formulation of it, and that a generally accepted physical understanding will be more quickly reached by agreement or disagreement with expressed opinions, than by waiting for the arrival of a full-grown theory. It has been an extraordinarily difficult task to express the ideas I intended, and I wish to thank Prof. D. R. Hartree for many valuable criticisms of my first attempts to do so, though he must be exonerated from all blame if the final result is unintelligible or erroneous. 1. The quantum mechanics have been expressed in a variety of ways, which place the emphasis differently, but it has been shown that they are all exactly equivalent, so what may choose which we will. I shall use the following description, limiting myself to the simpler cases which do not involve considerations of relativity. We take a partial differential equation of the wave type, set down according to certain rules depending on the particular system considered. We solve this subject to certain boundary conditions, expressive of all the limitations imposed by silts, mirrors, diffraction, gratings, moving shutters, etc., that may occur in the proposed system, and obtain as result the wave function Ψ, a function of all the co-ordinates of the system and of the time. From this we from a set of functions, of which the simplest is |Ψ|2; this process may be called taking the intensities. We next have to prepare for the particle aspect, by applying certain rules so as to normalise the intensities, a process entirely foreign to the idea of waves. Finally, we make the interpretation, in which we say that the normalised intensities measure the probability of the particles having such and such positions, momenta, energies, etc., and these are the results verified by observation.